Approximation Numbers in Some Weighted Function Spaces Original Research Article

In this paper we study weighted function spaces of type Bsp,q(Rn, w(x)) and Fsp,q(Rn, w(x)) where w(x) is a weight function of at most polynomial growth, preferably w(x) = (1 + |x|2)α/2 with α ∈ R. The main result deals with estimates for the approximation numbers of compact embeddings between spaces of this type. Furthermore we are concerned with the dependence of the approximation numbers a, of compact embeddings between function spaces Bsp,q(Ω) and Fsp,q(Ω) on an underlying domain Ω.